Math Snap

STEP 1

1. Gene claims that finding $25\%$ of a number is the same as dividing the number by $\frac{1}{4}$.
2. We need to verify whether this statement is true or false by comparing the results of both operations.

STEP 2

1. Define the mathematical expressions for both operations.
2. Calculate $25\%$ of a number.
3. Calculate the result of dividing the number by $\frac{1}{4}$.
4. Compare the results to determine if Gene's statement is correct.

STEP 3

Define the expressions for both operations. Let $n$ be the number in question.
- Finding $25\%$ of $n$ can be expressed as $0.25 \times n$.
- Dividing $n$ by $\frac{1}{4}$ can be expressed as $n \div \frac{1}{4}$.

STEP 4

Calculate $25\%$ of the number $n$.
$$25\% \text{ of } n = 0.25 \times n$$

STEP 5

Calculate the result of dividing $n$ by $\frac{1}{4}$.
$$n \div \frac{1}{4} = n \times 4$$

Compare the results from STEP_2 and STEP_3.
- $0.25 \times n$ is not equal to $n \times 4$.
Gene's statement is incorrect. Finding $25\%$ of a number is not the same as dividing the number by $\frac{1}{4}$. In fact, dividing by $\frac{1}{4}$ is equivalent to multiplying by $4$, which is quite different from finding $25\%$ of a number.